Random matrix approach to three-dimensional QCD with a Chern-Simons term

Abstract

We propose a random matrix theory for QCD in three dimensions with a Chern-Simons term at level $k$ which spontaneously breaks the flavor symmetry according to U($2N_{\mathrm{f}}$) $\to$ U($N_{\mathrm{f}}+k$)$\times$U($N_{\mathrm{f}}-k$). This random matrix model is obtained by adding a complex part to the action for the $k=0$ random matrix model. We derive the pattern of spontaneous symmetry breaking from the analytical solution of the model. Additionally, we obtain explicit analytical results for the spectral density and the spectral correlation functions for the Dirac operator at finite matrix dimension, that become complex. In the microscopic domain where the matrix size tends to infinity, they are expected to be universal, and give an exact analytical prediction to the spectral properties of the Dirac operator in the presence of a Chern-Simons term. Here, we calculate the microscopic spectral density. It shows exponentially large (complex) oscillations which cancel the phase of the $k=0$ theory.

28 pages, 11 figures

References in corpus (10)

• Non-Abelian Anyons and Topological Quantum Computation
• Center-stabilized Yang-Mills theory: confinement and large $N$ volume independence
• Effective Theory of Wilson Lines and Deconfinement
• New Phases of SU(3) and SU(4) at Finite Temperature
• Superbosonization of invariant random matrix ensembles
• Flavor and topological current correlators in parity-invariant three-dimensional QED
• Comparison of the superbosonization formula and the generalized Hubbard-Stratonovich transformation
• Dirac spectrum of one-flavor QCD at θ=0 and continuity of the chiral condensate
• QCD3 with Two-Index Quarks, Mirror Symmetry and Fivebrane anti-BIons near Orientifolds
• Symmetry Crossover Protecting Chirality in Dirac Spectra

Cited by in corpus (3)

• Metastable Vacua in Large-$N$ QCD${}_3$
• Cascade of phase transitions in a planar Dirac material
• Chiral random matrix theory for colorful quark-antiquark condensates